Well, are you looking to bridge the gap to fellow gun owners, or the gap within your own political beliefs?
I don't see any need to bridge political gaps with friends and neighbors. I don't see any need to bring politics into that at all, and if it is, there's no reason for a difference of opinion to be personal.
If it's in your own head, my suggestion is to reconcile emotion and logic. Write down what you feel the role of government should be, then examine the logic in each role and apply it consistently. Perhaps most important is actually understanding the design of the US government and the hypocracy inherent in both major political parties.
Hell, do one of those in-depth political identification tests. I worked with a guy who identified himself to anyone that would listen that he was a "paleo-con". But if you evaluated what he thought issue to issue, it turns out he was more a moderate Democrat. He was just so intent on being something, he didn't know what it actually was.